(I talk about the solution at length but nothing too close to blatant spoilers.)
At this point, I'm pretty sure I prefer H.M.'s impossibilities to Dr. Fell's, although I still do like both series equally. The truth behind the two "deaths without cause" is simple but brilliant - all the clues are there but darn if ya piece em together. The character of Herman Pennik must be one of the most interesting one-off characters in detective fiction, alongside Carr's own Fay Seton from He Who Whispers and Major Moon from Green for Danger. So evilly complex, so simply insinuating, and so cheerfully mad, Pennik and his supposed abilities are the real driving force of this story. There's also a small part of Pennik's character revealed at the end which reminds me of The Roman Hat Mystery if it had been done maybe a bit better - in this case there some interesting subversive tactics used around this aspect which you don't even realize. While at first I was not completely enamored by the reveal of whodunit (I mean, the cast of suspects is as limited as Green Capsule, which still gave me a sense of "why didn't I see it!",) there ended up being another level to that reveal which made it a lot better. The motive for the murders was something passed right under my nose but didn't really consider for certain reasons, and the motive for the impossibility, while parts of it are pretty obvious by halfway through, when the whole reason is shown is really brilliant. And the final reveal of H.M.'s reason for letting the media-circus over Teleforce happen was a really nice touch, especially when you consider the temporal setting of the book and the time it was published in. In that way I think it might surpass the ending of She Died a Lady for me. Some other aspects of the solution, like Pennik's mind-reading and the "astral projection", aren't too convincing but they make enough sense and honestly with how well-done everything else is I don't blame Carr for not knocking it out on every single mystery. Speaking of Green Capsule, this is definitely the Merrivale version of that. A complex, subtly clued crime (one of which on both counts took place in front of several witnesses) which has a rewarding solution on several counts. Highly recommended.
More spoiler-y side note - I actually thought I was really close with how the causeless deaths were done, and in a way I was. One aspect of the two victims, the Constables, are that they both had bad malaria in the past and still suffer side effects from it. I was convinced that somehow the murderer was enabling the Constables' malaria rebounds in the method of killing them, like some medical way they used their post-malaria weakness to kill them. Of course, in the solution it turns out that an aspect of their malaria rebound caused something to change in their house (rather than their actual physical health) which enabled the method of murder - a method which did not actually need the victim to have had malaria. So I was close... but not quite at the cigar. Sigh. Maybe one day I'll crack one of these cases.